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g A thin uniform cylindrical turntable of radius 2.4 m and mass 32 kg rotates in a horizontal plane with an initial angular speed of 10 rad/s. The turntable bearing is frictionless. A clump of clay of mass 13 kg is dropped onto the turntable and sticks at a point 1.7 m from the point of rotation. Find the angular speed of the clay and turntable. Answer in units of rad/s.

Sagot :

Answer:

Explanation:

Moment of inertia of the turntable I = 1/2 m R²

= 0.5 x 32 x 2.4²

= 92.16 kg m²

Moment of inertia of the turntable along with clamp of clay

= 1 /2 M R² + m r² where M and m are mass of turntable and clump of clay and R is radius of turntable , r is distance of clay from the axis of rotation .

= 0.5 x 32 x 2.4² + 13 x 1.7²

= 92.16 kg m² + 37.57 kg m²

= 129.73 kg m².

Apply law of conservation of angular momentum

I₁ ω₁ =I₂ω₂

I₁ =92.16 kg m² ω₁ = 10 rad/s I₂ = 129.73 kg m²; ω₂ = ?

92.16 kg m²  x  10 rad/s = 129.73 kg m² x ω₂

ω₂ = 7.10 rad /s .

the angular speed of the clay and turntable = 7.10 rad /s .

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